Question

Given X ~ B(n, P) if n = 25 and E(X) = 10, find p and SD(X).

Answer 1

Given: n = 25 and  E(X) = 10

E(X) = np

∴ 10 = 25 × p

∴ p = `10/25 = 2/5`

∴ q = 1 - p = `1 - 2/5 = 3/5`

Var(X) = npq

`= 25 × 2/5 × 3/5 = 6`

∴ SD(X) = `sqrt("Var"("X")) = sqrt6`

Hence, p = `2/5`, S.D.(X) = `sqrt6`